Exam 4: The Time Value of Money Part 2

Which of the following choices will result in a greater future value at age 65? Choice number 1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments) into an account and then leave it untouched until you are 65 (another 39 years). Choice number 2 is to begin at age 27 and make $3,000 deposits into an investment account every year until you are 65 years old (a total of 39 investments). Each account earns an average of 10% per year. (The investments are end-of-year payments.)

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay the interest of $8,000 at the end of each year prior to maturity and the final payment of $108,000 at the end of 10 years, then you have just repaid what type of loan?

Which of the following is NOT an example of ordinary annuity cash flows?

What type of loan makes interest payments throughout the life of the loan and then pays the principal and final interest payment at the maturity date?

At what interest rate would you be indifferent to a lottery payout today of $2,229,389.17, or 25 equal annual end-of-the-year payouts of $200,000?

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is an interest-only loan?

You have a choice between a lottery lump sum payout of $5,975,191.24 today or a series of twenty annual annuity payments of $500,000 each (first cash flow one year from today). At what discount rate are you indifferent between the two choices?

Given the following cash flows, what is the future value at year six when compounded at an interest rate of 8.0%?

A wealthy woman just died and left her pet cats the following estate: $50,000 per year for the next 15 years with the first cash flow today. At a discount rate of 3.2%, what is the feline estate worth in today's dollars?

After winning the lottery, you state that you are indifferent between receiving twenty $500,000 end-of-the-year payments (first payment one year from today), or a lump sum of $5,734,961 today. What interest rate are you using in your decision-making process such that you are indifferent between the two choices?

You are saving money for a down payment on a new house. You intend to place $5,000 at the end of each year for three years into an account earning 6% per year. At the end of the fourth year, you will place $10,000 into this account. How much money will be in the account at the end of the fourth year?

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years. If you discount these cash flows at an annual rate of 14%, what is the present value of your expected cash flows?

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars?

When solving for the future value of a stream of unequal cash flows, it is important to add the values together BEFORE applying the future value formula to determine their future value.

You have a choice between a lottery lump sum payout of $3,800,000 today or a series of twenty annual annuity due payments. At a discount rate of 6.00%, how large must the annual annuity due payments be to make you indifferent between the two choices? Use a calculator to determine your answer.

If we discount the annual payments from winning the lottery at 10%, the corresponding present value is greater than if we discount the annual payments at 12%.

Solving for an unknown interest rate given the PV, FV, PMT, and N is an iterative (or trial-and-error) process.

Ordinary annuity payments occur at the beginning of the period, whereas annuity due payments occur at the end of the period.

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay the total amount of principal and interest due of $215,892.50 at the end of 10 years, what type of loan did you have?

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the size of the annual ordinary annuity payment if the loan is amortized over a ten-year period at a rate of 8.50%?